Search & Filtering
A box of 15 peaches is ready for shipment and 3 of the peaches are defective. An inspector will
select at most 3 peaches from the box. He selects each peach randomly, one at a time, inspects it
and if it is not defective, he selects the next one. If he selects a defective peach, he stops the
process, and the box will not be shipped. If the first three peaches selected are good, he replaces the
3 peaches and ships the box.
1.1. Draw the tree diagram representing the outcome and assign probabilities.
1.2.What is the probability that the box is shipped?
1.3.What is the probability that the second peach is bad, or the 3
rd peach is good?
Determine whether the statement is logically equivalent using truth tables. [ (~P ∧ Q ) ⊕ P ] AND ( ~P V∧ Q)
find the intetest rate if $5000 is borrowed and $5243.75 is paid back 9 months later
Use Euclidean algorithm to determine the gcd (4076, 1024)
In a market survey conducted to examine whether the choice of a brand is related to the income levels of the consumers, a random sample of 400 consumers reveal the following:
Income level (per month) Brand 1 Brand 2 Brand 3 Total
<20000 93 72 75 240
20000-50000 50 35 37 122
>50000 12 15 11 38
Total 155 122 123 400
Test the association between income level and brand preference at 5% significant level.
An oil company sends out monthly statements to its customers who purchased gasoline and other items using the company’s credit card. Until now, the company has not included a pre-addressed envelope for returning payments. The mean number of days before payment is received is 9.8. As an experiment to determine whether enclosing pre-addressed envelopes speeds up payment, 150 customers selected at random were sent pre-addressed envelopes with their bills. The sample statistics showed a mean of 9.16 days and a standard deviation of 2.642 days. Do the data provide sufficient evidence at 5% level of significance to establish that enclosure of pre-addressed envelopes improves the average speed of payments?
A manufacturer of light bulbs claims that its light bulbs have a mean life of 2000 hours with a standard deviation of 2. A random sample of 200 such bulbs is selected for testing. If the sample produces a mean value of 1992 hours and a sample standard deviation of 81, is there sufficient evidence to claim that the mean life is significantly less than the manufacturer claimed at 5% significant level
A school has 1000 students. The principal of the school thinks that the average IQ of its students is at least 110. To prove her point, she administers an IQ test to 200 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 1%
a) Does the sequence (3+(-1)n) converge to 2? Justify.
b) Show that "\\lim _{x\\to \\infty }\\left(\\frac{x-3}{x+1}\\right)^x=e^{-4}"
c) Check whether the sequence fn (x) = "\\frac{3x}{1+nx^2}" where x ∈ [2,∞ [ is uniformly
convergent in [2,∞ [
In its first year, “Abol Buna Co” had the following experience Sales = 25,000 units
Selling price = br.100 TVC = br.1, 500,000 TFC = br.350, 000. Required:
(a) Develop Revenue, cost & profit functions for the co. in terms of quantity.
(b) Find the Breakeven point in terms of quantity
(c) Convert the cost equation in terms of quantity in to a cost equation in terms of revenue
(d) Find the Breakeven revenue
(e) If profit had been br. 500,000 what would have been the sales volume (revenue) &
the quantity of sales
(f) What would have been the profit if sales are br. 2,000,000?
